verification of the Gauss hypergeometric series (at the prototype stage)

kv/airy.hpp

verification of the Airy function (at the prototype stage)

kv/bessel.hpp

verification of the Bessel function of the first kind (at the prototype stage)

kv/geoseries.hpp

reliable computation of the sum of geometrical series, the common ratio of which is a interval

kv/matrix-inversion.hpp

a wrapper of ublas for computing (approximate) inverse matrix

kv/qr.hpp

(approximate) QR decomposition by the Gram-Schmidt orthogonalization

kv/vleq.hpp

verification of linear equations by a widely used method

kv/eig.hpp

The eigenpairs of an asymmetric real matrix are (approximately) computed by function "eig".
The eigenvalues of an asymmetric real matrix are computed with verification by function "veig".
They are produced by Akitoshi Takayasu.

kv/lp.hpp

verification of the simplex method for linear equations (without a sufficient test)

kv/optimize.hpp

to solve a optimization problems (without a sufficient test)

kv/kkt.hpp

to make a KKT equation from an objective function, an inequality constraint, and an equality constraint

kv/newton.hpp

the usual Newton method (without verification and a sufficient test)

kv/dka.hpp

function "dka" which performs the Durand Kerner Aberth method without verification and function "vdka" which verifies a solution by Smith's Theorem (without a sufficient test)

kv/cardano-ferrari.hpp

to compute solutions to a polynomial equation of degree 3 or 4 by the Cardano/Ferrari method

kv/highderiv.hpp

to compute higher-order differentials of a function with one variable, by a power series arithmetic

kv/matplotlib.hpp

simple graphics library using python and matplotlib

kv/psa-plot.hpp

to draw the psa types using matplotlib

kv/jointrange.hpp

to draw the joint range of affine arithmetic using matplotlib

kv/all.hpp

to include all files in directory "kv" (not recommended because of a long compilation time)

test/

tests of this library, and samples of calling each functions

almost all (but not entirely all) functions are included in these test programs

test/test-interval.cc

test of interval arithmetics

test/test-rounding.cc

simple test for confirming whether the rounding mode is correctly changed for the four arithmetic and square-root operations

test/test-nohwround.cc

test for the emulation of the changes of rounding modes provided by the option -DKV_NOHWROUND

test/test-fma.cc

simple test for confirming whether the fma instruction works correctly

test/test-dd.cc

test for the dd type

test/test-idd.cc

test for interval arithmetics with the double-double precision

test/test-mpfr.cc

test for mpfr

test/test-impfr.cc

test for interval arithmetics with mpfr

test/test-interval-conv.cc

test of interval-conv.hpp

test/test-complex.cc

test of complex numbers

test/test-autodif.cc

test of the automatic differentiation

test/test-affine.cc

test of the affine arithmetics

test/test-affine-reduce.cc

test of the function of reducing the dummy variables in affine arithmetics

test/test-affinemult.cc

test of the multiplication with affine arithmetic

test/test-psa.cc

test of psa

test/test-psa-history.cc

test of the function of history in psa

test/test-kraw-approx.cc

test of the Krawczyk method around an approximate solution for a nonlinear equation

test/test-allsol.cc

test of finding all solutions of a nonlinear equation

test/test-allsol-simple.cc

test of finding all solutions of a simplified nonlinear equation

test/test-allsol-affine.cc

test of allsol-affine.hpp

test/test-allsol-rest.cc

examples where an uncertain interval, which does not ensure both the existence and the non-existence of solution, is returned (e.g., in the case where there exists a multiple root)

test/test-allsol-infinity.cc

test of finding all solutions to a nonlinear equation on a unbounded domain

test/test-complexeq.cc

sample where a nonlinear equation on a complex domain is solved

test/test-ode.cc

test of ode.hpp

test/test-ode-autodif.cc

test of ode-autodif.hpp

test/test-ode-maffine.cc

test of ode-maffine.hpp

test/test-ode-callback.cc

sample where one specifies a callback function for ode-maffine and let ode-maffine do somethings while solving a equation at the same time.

test/test-ode-stop.cc

sample of stopping to solve ODE halfway on certain condition using
callback function.

test/test-ode-maffine2.cc

test of ode-maffine2.hpp

test/test-ode-affine.cc

tests of ode-affine.hpp and ode-affine-wrapper.hpp

test/test-ode-qr.cc

test of ode-qr.hpp

test/test-ode-lohner.cc

test of ode-lohner.hpp

test/test-ode-qr-lohner.cc

test of ode-qr-lohner.hpp

test/test-odescale.cc

test of odescale.hpp

test/test-ode-nv.cc

test of ode-nv.hpp

test/test-ode-autodif-nv.cc

test of ode-autodif-nv.hpp

test/test-rk.cc

test of rk.hpp

test/test-rkf45.cc

test of rkf45.hpp

test/test-strobomap.cc

test of strobomap.hpp

test/test-bvp.cc

sample where a two-point boundary value problem is solved using stroboscopic map

test/test-poincaremap.cc

test of poincaremap.hpp

test/test-defint.cc

test of defint.hpp

test/test-defint-byode.cc

sample where a integral is regarded as an ODE and computed by an ODE Solver

test/test-doubleintegral.cc

test of doubleintegral.hpp

test/test-defint-singular.cc

test of defint-singular.hpp

test/test-lobachevsky.cc

test of lobachevsky.hpp

test/test-gamma.cc

test of gamma.hpp

test/test-beta.cc

test of beta.hpp

test/test-hypergeom.cc

test of hypergeom.hpp

test/test-airy.cc

test of airy.hpp

test/test-bessel.cc

test of bessel.hpp

test/test-geoseries.cc

test of geoseries.hpp

test/test-invert.cc

test of matrix-inversion.hpp

test/test-qr.cc

test of qr.hpp

test/test-vleq.cc

test of vleq.hpp

test/test-eig.cc

test of eig.hpp

test/test-lp.cc

test of lp.hpp

test/test-optimize.cc

test of optimize.hpp

test/test-kkt.cc

test of kkt.hpp

test/test-newton.cc

test of newton.hpp

test/test-dka.cc

test of dka.hpp

test/test-cardano-ferrari.cc

test of cardano-ferrari.hpp

test/highderiv.cc

test of highderiv.hpp

test/test-matplotlib.cc

test of matplotlib.hpp

test/test-psa-plot.cc

test of psa-plot.hpp

test/test-ode-plot.cc

the orbit of a solution to an ODE is displayed by the use of callback of psa-plot.hpp and ode